In co-pending application Ser. No. 07/142,736, filed Jan. 11, 1988, and issued as U.S. Pat. No. 4,934,687 on Jun. 19, 1990, of Hayden et al., assigned to the same assignee as the present invention, there is disclosed a high-speed stacker. A stacker forms neat, stable, precisely aligned stacks of printed products from a high-speed press or bindery line. The products may comprise items such as printed book or magazine signatures, newspaper sections, magazine sections, inserts, etc. The stacker is capable of handling the output of a press producing as many as 80,000 such products per hour. It is among the objects of the present invention to provide a method, apparatus, and system for lifting and moving stacks for further processing. More specifically, the apparatus is designed to manipulate "cubes" consisting of four such stacks. The manner in which this is accomplished will become apparent from the following description, the accompanying drawings, and the appended claims.